A cyclic cohesive zone model is proposed to simulate the mode-I crack growth in quasibrittle structures under compressive fatigue. The constitutive behavior of the cohesive elements is formulated for both tension and compression regimes. A strain-softening cohesive law is adopted for the tension regime whereas a plastic-type cohesive behavior is considered for the compression regime. It is shown that the proposed model is able to capture some essential fracture behaviors of quasibrittle structures under compressive fatigue, which include the onset of fatigue crack growth, the gradual decrease in crack growth rate, and the exhaustion of residual tensile stress over the cycles. Based on a fracture process zone (FPZ)-equivalence principle, it is further shown that the existing kinetics equation for tensile fatigue crack can be extended to the crack growth under cyclic compression.